What is the integral of e^{-inx} ?

The integral of e^{-inx} is 1/n sin(nx)+i 1/n cos(nx)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-inx}

\int e^{- in x} d x

\frac{1}{n} sin (n x) + i \frac{1}{n} cos (n x) + C

Solution steps

\int e^{- in x} d x

Simplify

e^{- in x} : cos (n x) - i sin (n x)

= \int cos (n x) - i sin (n x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (n x) d x - \int i sin (n x) d x

\int cos (n x) d x = \frac{1}{n} sin (n x)

\int i sin (n x) d x = - i \frac{1}{n} cos (n x)

= \frac{1}{n} sin (n x) - (- i \frac{1}{n} cos (n x))

Simplify

\frac{1}{n} sin (n x) - (- i \frac{1}{n} cos (n x)) : \frac{1}{n} sin (n x) + i \frac{1}{n} cos (n x)

= \frac{1}{n} sin (n x) + i \frac{1}{n} cos (n x)

Add a constant to the solution

= \frac{1}{n} sin (n x) + i \frac{1}{n} cos (n x) + C

\int (sin (x) - cos (x)) d x

\int x^{2} cos (n) x d x

x \to 6 lim (- 2 x - 5)

f (t) = (e^{t} - e^{- t})^{2}

y^{^{'}} + 8 y = 3 x

What is the integral of e^{-inx} ?
The integral of e^{-inx} is 1/n sin(nx)+i 1/n cos(nx)+C